On the structure of singularities of integrable Schrödinger operators

DOI10.1023/A:1007656025201zbMath0969.47018OpenAlexW171151318MaRDI QIDQ1590365

Yuri Yu. Berest, Alexander P. Veselov

Publication date: 23 September 2001

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1007656025201

zbMATH Keywords

Darboux transformationinverse scattering transformationclassification of the D-integrable modelsD-integrabilitygeodesic hypersurfacesHadamard problemn-dimensional Schrödinger operatorSchrödinger's factorizationWitten's supersymmetric quantum mechanics

Mathematics Subject Classification ID

Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) General theory of partial differential operators (47F05) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Complex surface and hypersurface singularities (32S25) Commutative rings of differential operators and their modules (13N10) Scattering theory of linear operators (47A40) Critical points of functions and mappings on manifolds (58K05)

Related Items (5)

Differential operators on the superline, Berezinians, and Darboux transformations ⋮ Ideals of differential operators and transformations of linear partial differential equations ⋮ Classification of multidimensional Darboux transformations: first order and continued type ⋮ Classification of Darboux transformations for operators of the form \(\partial_x\partial_y+a\partial_x+b\partial_y+c\) ⋮ Differential transformations of parabolic second-order operators in the plane

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